A linear guide SOMC design method, device, medium and program product

Abstract

This invention discloses a linear guide rail SOMC design method, equipment, medium, and program product, including: (1) constructing a simulation model and SOMC design model with static stiffness as the target and weight and maximum contact stress as constraints based on the structural characteristics and static load analysis of the linear guide rail; (2) constructing a design space, generating an initial population and establishing a database, and obtaining a set of high-influence continuous variables and a set of high-influence discrete variables through SRC and CEA sensitivity analysis methods; (3) generating corresponding candidate sets based on the two sets of variables, and obtaining a complete set of candidate guide rails through individual pairing; (4) establishing a random forest prediction model, screening excellent subsets and selecting the best offspring guide rails; (5) updating the database and prediction model after simulation evaluation, returning to step (3) until the indicators meet the standards, and outputting the optimal parameter values. This invention can effectively balance the SOMC process with stiffness as the optimization target and weight and maximum contact stress as constraints, achieving higher accuracy and better overall performance.

Description

Technical Field

[0001] This invention relates to the fields of general artificial intelligence technology and swarm intelligence, and more specifically, to a linear guide SOMC (Single-Objective with Multiple Constraints) design method, device, medium, and program product. Background Technology

[0002] Linear guides are key components in precision equipment transmission systems, determining positioning accuracy and load-bearing capacity. They are widely used in high-end precision equipment fields such as CNC machine tools, industrial robots, and automated production lines. The static stiffness of linear guides directly affects the overall rigidity and motion stability of the machine; the maximum contact stress directly relates to the fatigue life and safety margin of components; and the weight determines the inertia and dynamic response speed of the transmission system. With the development demands for high rigidity, long lifespan, and lightweight in high-end precision equipment, how to optimize static stiffness while keeping the maximum contact stress and weight within a safe and reasonable range has become a core challenge in the structural design of linear guides.

[0003] Current traditional linear guide design methods largely rely on experience-based design, benchmarking and imitation of similar products, or repeated finite element simulations. These traditional methods typically only allow adjustment of single structural parameters, making it difficult to achieve global optimization of target performance under multiple constraints. Furthermore, the lack of selection of design variables leads to high redundancy in the optimization space, massive computational scale, numerous iterations, high computational costs, and long development cycles, making it difficult to quickly obtain the optimal solution that meets engineering requirements.

[0004] With the development of data-driven and intelligent optimization technologies, optimization methods based on machine learning surrogate models have gradually become an important tool in structural design. Random forest surrogate models possess strong nonlinear fitting capabilities and generalization performance, enabling the rapid establishment of nonlinear mapping relationships between design variables and static stiffness, maximum contact stress, and weight. This effectively replaces time-consuming simulations and significantly improves optimization efficiency. However, considering the mixed variable characteristics of continuous and discrete variables in linear guide rail design, conventional single evolutionary algorithms struggle to adapt to the update mechanisms of different variable types, necessitating the development of more accurate and efficient hybrid evolutionary strategies.

[0005] Although existing intelligent optimization methods have been applied in some engineering fields, they still have significant limitations in the single-objective multi-constraint optimization of linear guides: First, the lack of a key design variable screening mechanism based on sensitivity analysis leads to low optimization efficiency; second, the absence of a co-evolutionary framework combining diverse potential-driven and probability-driven algorithms for mixed variables makes it difficult to balance global optimization with the rationality of variable updates; third, the lack of a fast non-dominated sorting algorithm for effectively screening excellent offspring solutions during multi-constraint optimization; and fourth, the failure to determine a unique optimal solution from the non-dominated solution set through statistical ranking makes it difficult to directly apply the optimization results to engineering applications. Summary of the Invention

[0006] In view of the above limitations of the existing technology, and considering the design requirements of linear guides to maximize static stiffness while being subject to the optimization objectives of maximum contact stress and weight constraints, this invention proposes a linear guide SOMC design method, equipment, medium and program product.

[0007] To achieve the above objectives, the first aspect of the present invention provides a linear guide rail optimization design method, the method comprising the steps of: S1 uses the linear guide rail dimensions (continuous variables) and material type, preload level, and number of sliders and balls (discrete variables) as design parameters. Based on structural characteristics and static load analysis, a simulation model and SOMC design model are constructed with static stiffness as the objective and weight and maximum contact stress as constraints. S2. Construct a design space based on the range of design parameters, generate an initial population and establish a database using chaotic strategy and full factorial design, and obtain the set of high-impact continuous variables and the set of high-impact discrete variables through SRC and CEA sensitivity analysis methods, respectively. S3, based on a set of high-impact continuous variables and a set of high-impact discrete variables, generates candidate sets of continuous and discrete variables through a diversity potential-driven evolutionary mechanism and a statistical probability-driven mutation strategy, respectively, and obtains a candidate guide set through individual pairing; S4. Establish a random forest prediction model with objectives and constraints. Select an excellent subset from the candidate guide set through fast non-dominated sorting, and then select the best offspring guide by combining statistical ranking method. S5. Use the simulation model to evaluate the best offspring guide rail, update the database and random forest prediction model, return to step S3, until the index is met, and output the optimal parameter values.

[0008] Optionally, step S1 specifically includes the following steps: S1.1, combining the structural characteristics of linear guide rails, the slider length, slider width, slider height, raceway curvature radius, raceway center distance, initial contact angle, raceway groove depth, ball diameter, guide rail length, guide rail width, and guide rail height are taken as continuous variables, while the number of balls, number of sliders, material type, and preload level are taken as discrete variables. The continuous and discrete variables are used as design parameters. S1.2, Based on the load conditions of the linear guide structure, a three-dimensional model is constructed using the three-dimensional modeling software Catia and parameterized to obtain a parameterized model; S1.3, import the parametric model, the load conditions of the linear guide structure and the key boundary conditions into the finite element analysis pre- and post-processing software Ansys Workbench for finite element analysis to obtain the finite element analysis model; S1.4. Using the solver of the structural optimization and multiphysics simulation software, static load analysis is performed on the finite element analysis model to obtain the static stiffness, maximum contact stress and weight simulation model of the linear guide rail. S1.5, Based on the simulation model of static stiffness, maximum contact stress, and weight of the linear guide, the SOMC design model of the linear guide is constructed with static stiffness as the objective and maximum contact stress and weight as constraints. The specific expressions are as follows: , , , In the above formula, This indicates the search for the optimal solution to the design parameters. This indicates the design parameters of the linear guide. Indicates the length of the slider. Indicates the height of the slider. Indicates the slider width. Indicates the radius of curvature of the raceway. Indicates the center distance of the raceways. Indicates the initial contact angle. Indicates the depth of the raceway groove. Indicates the length of the guide rail. Indicates the guide rail height. Indicates the width of the guide rail. Indicates the diameter of the ball bearing. Indicates the number of balls. Indicates the number of sliders. Indicates the material type. Indicates the preload level. This indicates finding the maximum value. This indicates the design parameters of the linear guide. The corresponding static stiffness at that time This indicates the design parameters of the linear guide. The corresponding static stiffness function at time, This represents the constraints that the linear guide rail must satisfy regarding its weight and maximum contact stress. This indicates the design parameters of the linear guide. The maximum contact stress corresponding to this time, Indicates the maximum contact stress threshold. This indicates the design parameters of the linear guide. The corresponding weight at that time This indicates the weight threshold.

[0009] Optionally, step S2 specifically includes the following steps: S2.1, Determine the range of values ​​for continuous variables and the set of values ​​for discrete variables according to design requirements, and construct continuous design space and discrete design space respectively; S2.2 An initial population of discrete variables is generated in the discrete design space using full factorial design, and an initial population of continuous variables is generated in the continuous design space using a chaotic strategy. The discrete and continuous variable populations constitute the initial population, where the chaotic sequence is generated by the Tent mapping criterion. Different initial chaotic sequence values ​​are designed for each design parameter of each continuous variable. The initial chaotic sequence value is iteratively updated, and the next chaotic sequence value is obtained through piecewise calculation. The formula for calculating chaotic sequences is as follows: , , In the above formula, Indicates the first The nth continuous variable Chaotic sequence values ​​corresponding to each design parameter This represents the Tent mapping criterion function. Indicates the first The nth continuous variable Chaotic sequence values ​​corresponding to each design parameter This represents the chaotic sequence mapped to the initial population. Indicates the initial population size. Indicates the dimension of the initial population; S2.3, with the optimization objective of maximizing static stiffness and the constraints of the maximum contact stress not exceeding the maximum contact stress threshold and the weight not exceeding the weight threshold, the initial population is simulated and evaluated using the static stiffness function, maximum contact stress function, and weight function of the linear guide. The obtained static stiffness, maximum contact stress, and weight data of the linear guide are used as real samples to establish a database. Then, the initial population is divided into a set of preprocessed continuous variables and a set of preprocessed discrete variables. For the two sets of variables, the target values ​​of their corresponding parameters and the output response sets of each constraint index are determined respectively. S2.4, For the preprocessed continuous variable set, based on the SRC sensitivity analysis method, firstly, each continuous variable is standardized. Then, a linear regression model is constructed using the output response set of the preprocessed continuous variables as the dependent variable and the standardized continuous variables as the independent variables. The regression coefficients are obtained by fitting the linear regression model using the least squares method. The formulas for the standardization operation and the linear regression model are as follows: , , In the above formula, Indicates the first Standardized values ​​of a continuous variable. No. The original observations of a continuous variable, Indicates the first The mean of a continuous variable, Indicates the first The sample standard deviation of a continuous variable. This represents the set of outputs corresponding to a sample containing all preprocessed continuous variables. This represents a linear regression model that includes all preprocessed continuous variables. This represents the intercept of the linear regression model. Indicates the first Standard regression coefficients of continuous variables Indicates the number of continuous variables. Represents the residuals of a linear regression model; S2.5, the obtained standard regression coefficients Take the absolute value, then sort in descending order. Based on engineering experience, set the threshold for the regression coefficients of continuous variables as follows: A higher ranking indicates a greater impact of the continuous variable on the output; therefore, those that meet the criteria are selected. High-impact continuous variable set with threshold requirements ; S2.6, For the preprocessed set of discrete variables, based on the CEA sensitivity analysis method, the sum of squares of the main effects of each discrete variable is calculated according to the output response set. and the sum of squares of the interaction effects between the two discrete variables. The contribution of each discrete variable is calculated from the sum of squares of the two effects. The CEA sensitivity analysis formula is as follows: , , , In the above formula, Indicates the first Sum of squares of the main effects of discrete variables Indicates the first The i-th discrete variable The static stiffness value of the guide rail at each level. Indicates the first The number of experiments at a certain level for a discrete variable. Indicates the first under all experimental combinations The static stiffness value of the guide rail at each level. Indicates the total number of experiments. Indicates the first The expression for the between-group variance of discrete variables. No. The discrete variable and the first The sum of squares of the interaction effects of discrete variables, Indicates the first The discrete variable and the first The first discrete variable combination The static stiffness value of the guide rail at each level. Indicates the first The discrete variable and the first The number of experiments at a certain level under a combination of discrete variables. Indicates the first The i-th discrete variable The static stiffness value of the guide rail at each level. This represents the total variance including all preprocessed discrete variables. Indicates the first The main effect contribution of each discrete variable Indicates the first The discrete variable and the first The contribution of the interaction effect of each discrete variable; S2.7, Contribution of the main effects to all discrete variables Sort in descending order and set the main effect screening threshold to [value]. The higher the ranking of the discrete variable, the greater its impact on the target. Variables that meet the criteria are selected. Candidate set of main effect discrete variables with threshold requirements Subsequently, the contribution of the interaction effect to all discrete variables. Sort in descending order and set the interactive effect screening threshold to [value]. Filter out those that meet the requirements For high-contribution interaction parameter pairs that meet the threshold requirements, extract all parameters from the high-contribution interaction parameter pairs to form a candidate set of discrete variables for interaction effects. ,Pick and The union of these sets yields the set of high-impact discrete variables. If the candidate set of discrete variables for interaction effects The parameters in were not entered. However, if it exists in multiple high-contribution interaction parameter pairs, then it will be added to the list. This ensures that both the core parameters dominated by the main effect and the key correlation parameters dominated by the interaction effect are taken into account.

[0010] Optionally, step S3 specifically includes the following steps: S3.1, for populations containing only high-influence continuous variables, using the static stiffness objective function of the linear guide rail as the core, sorts the current generation of continuous variable populations in descending order, and uses the Epsilon constraint method to sort the current generation of populations... Extract three individual sets , , The specific formula for the Epsilon constraint method is as follows: , In the above formula, Indicates the current generation population The extraction level is A collection of individuals Indicates the contemporary population individuals, Indicates the contemporary population The total number of individuals, Indicates the level as The constraint threshold of the individual set, Represented as an individual The serial numbers are sorted in descending order of static stiffness. Indicates the level as The constraint threshold of the individual set, where The value is 0.1. The value is 0.2. The value is 0.3; S3.2, from each individual set In sequence, an individual is randomly selected as the reference individual vector for the optimal, second-optimal, and third-optimal static stiffness values. Then, a diversity potential-driven evolutionary mechanism is designed, which includes three evolutionary operations, namely the vectors of each of the remaining ordinary individuals. Based on the reference individual vector Evolutionary operations are performed in each direction to generate three candidate guideway positions. The evolutionary operation formula for each reference individual vector is as follows: , , , , In the above formula, Indicates to The first level of learning Candidate guide rail position, Indicates to The first level of learning Candidate guide rail position, Indicates to The first level of learning Candidate guide rail position, This indicates that the location needs to be updated. Substitute ordinary individual vectors, Indicates from A collection of individuals of a certain level The optimal linear guide individual randomly selected from the pool, i.e. , Indicates from A collection of individuals of a certain level The suboptimal linear guide individual randomly selected from the pool, i.e. , Indicates from A collection of individuals of a certain level The third best linear guide individual randomly selected from the pool, i.e. , and They represent the corresponding The first and second random coefficients are hierarchical and independent of each other. Indicates the first The convergence factor of the generation, Indicates the current iteration number. Indicates the maximum number of iterations; S3.3, based on the three candidate guide rail positions, the potential of each candidate guide rail is determined according to fitness calculation. Based on the objective function of maximizing static stiffness, the objective function of static stiffness is integrated with the constraint conditions composed of maximum contact stress constraint and weight constraint. A comprehensive fitness function is constructed based on the penalty coefficient, which serves as the evaluation benchmark for the potential of the candidate guide rail. The specific formula is as follows: , In the above formula, Indicates by The fitness function guides the evolutionary direction; the smaller the fitness value, the better the potential of the guided individual. Indicates from The static stiffness value of a guide rail individual randomly selected from the set of individuals of the grade. Indicates from The guide rail individuals are randomly selected again from the set of individuals of the grade, among which , This indicates finding the maximum value. Indicates the maximum contact stress threshold. express The corresponding maximum contact stress, Indicates the weight threshold. express The corresponding weight, This represents the penalty coefficient used to quantify the effect of maximum contact stress on individual fitness. This represents the penalty coefficient used to quantify the effect of weight on an individual's fitness. S3.4, based on the fitness function value for each evolutionary direction, calculate the weight coefficients of the candidate orbital positions obtained through the three evolutionary operations, where... The formula for calculating the weighting coefficients is as follows: In the above formula, Indicates the use of quantization The weighting coefficients, Indicates by Fitness values ​​that guide evolutionary direction based on level. Indicates by Fitness values ​​that guide evolutionary direction based on level. Indicates by Fitness values ​​guide the evolutionary direction based on rank; weight coefficients are obtained for other candidate orbital positions, and the final evolutionary formula is derived based on these weight coefficients, as follows: , In the above formula, This represents the generation of the first generation guided by each evolutionary direction. The effective child trajectories are obtained, that is, the candidate set of continuous variables. Indicates the first The weighting coefficients of each candidate guide rail position. Indicates the first The generation One candidate guide rail position; S3.5 For a population containing only a set of high-impact discrete variables, sort them in descending order according to the static stiffness target value to form an ordered set of guide rail candidates. Select the top a% of guide rails from the candidate set as the high-quality sample set. S3.6 Based on the obtained high-quality sample set, design a statistical probability-driven mutation strategy. Obtain the probability of each discrete variable in the high-quality sample set by statistically analyzing the frequency of occurrence of each discrete value. Divide the corresponding evolutionary intervals for each discrete value. The probability calculation formula is as follows: , , In the above formula, Indicates the first The i-th discrete variable takes the i-th... The probability of taking a discrete value. Indicates the first The discrete variables are listed first. Choose the first of the high-quality guide rails Frequency of discrete values Indicates the first Before the discrete variables All possible values ​​for a high-quality guide rail This represents the total number of high-quality guide rails selected from the current generation of guide rail library, sorted by static stiffness from largest to smallest. Indicates the first The i-th discrete variable takes the i-th... The cumulative probability for each discrete value. Indicates the first The i-th discrete variable takes the i-th... The cumulative probability of taking a discrete value; S3.7, according to the index of the discrete variable's value, define the evolution interval based on the probability of each discrete variable taking each discrete value. By generating uniformly distributed random numbers The values ​​of the discrete child guide rails on the corresponding discrete variables are determined by interval matching, as expressed by the formula: , In the above formula, Represented as the first Uniformly random numbers within the interval (0,1) generated independently by each discrete variable. Indicates the first The index of the final value selected by a discrete variable in the discrete child guide, i.e., the random number. The first matching when falling into the corresponding evolutionary range Each discrete value index is used to generate a random number from each discrete variable. The set of discrete values ​​that match the generated value index is the candidate set of the discrete variable; S3.8, through individual pairing, matches and integrates the structural features corresponding to discrete variables with the size parameters corresponding to continuous variables to form the first... A complete set of candidate guide rails with unified parameters This ensures that discrete and continuous variables are physically compatible and mechanically matched in terms of the design parameter values.

[0011] Optionally, step S4 specifically includes the following steps: S4.1 Select the guide rail sample dataset that has passed finite element simulation verification as historical samples. Each sample group contains input features and output labels, where the input features are the high-influence mixed variable set of the guide rail. The high-impact continuous variable set and the high-impact discrete variable set are integrated into a high-impact mixed variable set, and the output labels are... ,in This indicates the design parameters of the linear guide. The corresponding static stiffness value at that time This indicates the design parameters of the linear guide. The maximum contact stress corresponding to this time, This indicates the design parameters of the linear guide. The corresponding weight at that time was then used to divide the training set into several parts according to a certain ratio. and test set ; S4.2, construct three independent random forest prediction models RF0, RF1, and RF2 for the target value and constraint index respectively, and train the models. RF0 represents the random forest prediction model for predicting static stiffness value, RF1 represents the random forest prediction model for predicting maximum contact stress, and RF2 represents the random forest prediction model for predicting weight. S4.3 Calculate the coefficients of determination using the test set for the three trained random forest prediction models. Root mean square With mean absolute percentage error If the model's accuracy is not up to standard, supplement with high-discrepancy samples and perform hyperparameter tuning until the model's accuracy meets the standard. S4.4, for the newly generated first... Candidate guide rail set The static stiffness, maximum contact stress, and weight are predicted using a random forest prediction model to obtain the target values ​​and constraint indices for the candidate guide rail set. The predicted target values ​​and constraint indices are then unified into a minimization objective, transforming the problem into a three-objective problem. The predicted values ​​for the three objectives are: ,in This represents the predicted values ​​for the three objectives. Indicates the first in the candidate guide rail set One effective child guide rail, Indicates the first Predicted static stiffness values ​​of an effective descendant guide rail. Indicates the first Predicted maximum contact stress value for each effective descendant guide rail Indicates the first The predicted weight values ​​of each effective child guide rail are used as a benchmark for fast non-dominated sorting, resulting in a sample size of [number missing]. The Excellent sub-generation guide rail set ; S4.5, extract the target prediction values ​​of the excellent subset and perform linear normalization to map each target value to the [0,1] interval, eliminating the differences in dimensionality and order of magnitude between different targets, and ensuring the fairness of the weights of each indicator when selecting the best among multiple targets in the future. The normalization formula is as follows: , In the above formula, Indicates the first The generation The first excellent offspring guide rail in Normalized target value on each objective, Indicates the first The generation The first excellent offspring guide rail in Predicted values ​​for each target express Within the excellent subset The minimum predicted value of each target. express Within the excellent subset The maximum predicted value of each target; S4.6, normalization objective value The set of excellent descendant guide rails is comprehensively evaluated based on statistical ranking. The comprehensive score of each excellent descendant guide rail is calculated according to the scoring formula and sorted in ascending order. The lower the score, the better the comprehensive performance. The scoring formula is as follows: , In the above formula, Indicates the first The generation The overall score of each excellent descendant guide rail ranges from [0,1]. The smaller the value, the better the overall performance of the descendant guide rail. Indicates the first The weighting coefficients of each objective; S4.7 Select the best offspring guide rail with the lowest comprehensive score as the optimal offspring guide rail. If multiple excellent offspring guide rails have the same lowest comprehensive score, store them in a set of equally excellent offspring guide rails. Further filter the optimal offspring guide rail for the current generation using the target value difference formula, where the target value difference formula is as follows: , In the above formula, Indicates iteration to the th The best offspring guide for the generation, This represents the set of outstanding offspring guide rails that have the same minimum overall score. , Indicates the first generation to the first The mean of the three-objective normalized objective values ​​of the three parallel excellent offspring guides is calculated. This indicates the selection of the best child guide set. The minimum mean of the three objective values ​​after normalization.

[0012] Optionally, step S5 specifically includes the following steps: S5.1, The optimal offspring guide rail is evaluated using the aforementioned simulation model to obtain the optimal offspring guide rail. The corresponding target values ​​and constraint indicators are the static stiffness, maximum contact stress, and weight of the linear guide rail. S5.2, select the best offspring guide rail The corresponding target values ​​and constraint indicators are stored in the database, and the three random forest prediction models are updated based on all individual vectors in the database. S5.3, Determine the optimal offspring guide rail Does the corresponding static stiffness, maximum contact stress, and weight satisfy the optimization requirement of maximizing the static stiffness value under the constraints of minimizing weight and minimizing maximum contact stress? If so, output the optimal parameter values; otherwise, return to step S3 to continue iterative optimization until all optimization requirements are met, and output the optimal parameter values.

[0013] Secondly, the present invention provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the aforementioned linear guide SOMC design method.

[0014] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the aforementioned linear guide SOMC design method.

[0015] Fourthly, the present invention provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the aforementioned linear guide SOMC design method.

[0016] In summary, compared with the prior art, the technical solutions conceived in this invention have the following main advantages: 1. To address the limitations of existing technologies that fail to address the characteristics of mixed variables through co-evolution and struggle to balance global optimization and variable update rationality under single-objective, multi-constraint conditions, this invention constructs diversified potential-driven mechanisms and statistical probability-driven mutation strategies based on design variable types and sensitivity analysis results. During optimization, this approach accelerates convergence to the optimal design region while maintaining effective searching of the potential high-quality solution space, thus achieving a stable balance between convergence performance and search breadth.

[0017] 2. To address the limitations of traditional linear guide design methods, which rely excessively on time-consuming simulations and struggle to achieve optimal overall performance across static stiffness, maximum contact stress, and weight, this invention employs a random forest prediction model for rapid and accurate prediction of objectives and constraints. This is combined with fast non-dominated sorting to select the best offspring solution set, and a statistical ranking method is used to determine the optimal offspring guide. While ensuring prediction accuracy and optimization efficiency, this approach reliably achieves global coordination between single objectives and multiple constraints, resulting in a linear guide design scheme with stronger engineering applicability and superior overall performance.

[0018] In summary, this invention effectively addresses the challenges of optimizing linear guide structures involving high-precision simulations, adapting to complex design scenarios with multiple constraints and conflicting performance objectives, achieving higher optimization accuracy and more stable overall performance. This invention employs static stiffness as the optimization objective and maximum contact stress and weight as constraints to conduct integrated collaborative optimization, achieving optimal overall performance of the linear guide. It also provides a general and scalable technical framework for single-objective, multi-constraint optimization design of other precision mechanical structures. Attached Figure Description

[0019] Figure 1 A simplified flowchart of a linear guide SOMC design method provided by the present invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0021] Please see Figure 1 This invention provides a linear guide optimization design method, applicable to single-objective multi-constraint optimization design of linear guides. Specifically, the method includes steps S1 to S5.

[0022] S1 uses the linear guide rail dimensions (continuous variables) and material type, preload level, and number of sliders and balls (discrete variables) as design parameters. Based on structural characteristics and static load analysis, a simulation model and SOMC design model are constructed with static stiffness as the objective and weight and maximum contact stress as constraints.

[0023] The specific steps of step S1 are as follows: S1.1, combining the structural characteristics of linear guide rails, the slider length, slider width, slider height, raceway curvature radius, raceway center distance, initial contact angle, raceway groove depth, ball diameter, guide rail length, guide rail width, and guide rail height are taken as continuous variables, while the number of balls, number of sliders, material type, and preload level are taken as discrete variables. The continuous and discrete variables are used as design parameters. S1.2, Based on the load conditions of the linear guide structure, a three-dimensional model is constructed using the three-dimensional modeling software Catia and parameterized to obtain a parameterized model; S1.3, import the parametric model, the load conditions of the linear guide structure and the key boundary conditions into the finite element analysis pre- and post-processing software Ansys Workbench for finite element analysis to obtain the finite element analysis model; S1.4. Using the solver of the structural optimization and multiphysics simulation software, static load analysis is performed on the finite element analysis model to obtain the static stiffness, maximum contact stress and weight simulation model of the linear guide rail. S1.5, Based on the simulation model of static stiffness, maximum contact stress, and weight of the linear guide, the SOMC design model of the linear guide is constructed with static stiffness as the objective and maximum contact stress and weight as constraints. The specific expressions are as follows: , , , In the above formula, This indicates the search for the optimal solution to the design parameters. This indicates the design parameters of the linear guide. Indicates the length of the slider. Indicates the height of the slider. Indicates the slider width. Indicates the radius of curvature of the raceway. Indicates the center distance of the raceways. Indicates the initial contact angle. Indicates the depth of the raceway groove. Indicates the length of the guide rail. Indicates the guide rail height. Indicates the width of the guide rail. Indicates the diameter of the ball bearing. Indicates the number of balls. Indicates the number of sliders. Indicates the material type. Indicates the preload level. This indicates finding the maximum value. This indicates the design parameters of the linear guide. The corresponding static stiffness at that time This indicates the design parameters of the linear guide. The corresponding static stiffness function at time, This represents the constraints that the linear guide rail must satisfy regarding its weight and maximum contact stress. This indicates the design parameters of the linear guide. The maximum contact stress corresponding to this time, Indicates the maximum contact stress threshold. This indicates the design parameters of the linear guide. The corresponding weight at that time This indicates the weight threshold.

[0024] S2. Construct a design space based on the range of design parameters, generate an initial population and establish a database using chaotic strategy and full factorial design, and obtain the set of high-impact continuous variables and the set of high-impact discrete variables through SRC and CEA sensitivity analysis methods, respectively.

[0025] The specific steps of step S2 are as follows: S2.1, Determine the range of values ​​for continuous variables and the set of values ​​for discrete variables according to design requirements, and construct continuous design space and discrete design space respectively; S2.2 An initial population of discrete variables is generated in the discrete design space using full factorial design, and an initial population of continuous variables is generated in the continuous design space using a chaotic strategy. The discrete and continuous variable populations constitute the initial population, where the chaotic sequence is generated by the Tent mapping criterion. Different initial chaotic sequence values ​​are designed for each design parameter of each continuous variable. The initial chaotic sequence value is iteratively updated, and the next chaotic sequence value is obtained through piecewise calculation. The formula for calculating chaotic sequences is as follows: , , In the above formula, Indicates the first The nth continuous variable Chaotic sequence values ​​corresponding to each design parameter This represents the Tent mapping criterion function. Indicates the first The nth continuous variable Chaotic sequence values ​​corresponding to each design parameter This represents the chaotic sequence mapped to the initial population. Indicates the initial population size. Indicates the dimension of the initial population; S2.3, with the optimization objective of maximizing static stiffness and the constraints of the maximum contact stress not exceeding the maximum contact stress threshold and the weight not exceeding the weight threshold, the initial population is simulated and evaluated using the static stiffness function, maximum contact stress function, and weight function of the linear guide. The obtained static stiffness, maximum contact stress, and weight data of the linear guide are used as real samples to establish a database. Then, the initial population is divided into a set of preprocessed continuous variables and a set of preprocessed discrete variables. For the two sets of variables, the target values ​​of their corresponding parameters and the output response sets of each constraint index are determined respectively. S2.4, For the preprocessed continuous variable set, based on the SRC sensitivity analysis method, firstly, each continuous variable is standardized. Then, a linear regression model is constructed using the output response set of the preprocessed continuous variables as the dependent variable and the standardized continuous variables as the independent variables. The regression coefficients are obtained by fitting the linear regression model using the least squares method. The formulas for the standardization operation and the linear regression model are as follows: , , In the above formula, Indicates the first Standardized values ​​of a continuous variable. No. The original observations of a continuous variable, Indicates the first The mean of a continuous variable, Indicates the first The sample standard deviation of a continuous variable. This represents the set of outputs corresponding to a sample containing all preprocessed continuous variables. This represents a linear regression model that includes all preprocessed continuous variables. This represents the intercept of the linear regression model. Indicates the first Standard regression coefficients of continuous variables Indicates the number of continuous variables. Represents the residuals of a linear regression model; S2.5, the obtained standard regression coefficients Take the absolute value, then sort in descending order. Based on engineering experience, set the threshold for the regression coefficients of continuous variables as follows: A higher ranking indicates a greater impact of the continuous variable on the output; therefore, those that meet the criteria are selected. High-impact continuous variable set with threshold requirements ; S2.6, For the preprocessed set of discrete variables, based on the CEA sensitivity analysis method, the sum of squares of the main effects of each discrete variable is calculated according to the output response set. and the sum of squares of the interaction effects between the two discrete variables. The contribution of each discrete variable is calculated from the sum of squares of the two effects. The CEA sensitivity analysis formula is as follows: , , , In the above formula, Indicates the first Sum of squares of the main effects of discrete variables Indicates the first The i-th discrete variable The static stiffness value of the guide rail at each level. Indicates the first The number of experiments at a certain level for a discrete variable. Indicates the first under all experimental combinations The static stiffness value of the guide rail at each level. Indicates the total number of experiments. Indicates the first The expression for the between-group variance of discrete variables. No. The discrete variable and the first The sum of squares of the interaction effects of discrete variables, Indicates the first The discrete variable and the first The first discrete variable combination The static stiffness value of the guide rail at each level. Indicates the first The discrete variable and the first The number of experiments at a certain level under a combination of discrete variables. Indicates the first The i-th discrete variable The static stiffness value of the guide rail at each level. This represents the total variance including all preprocessed discrete variables. Indicates the first The main effect contribution of each discrete variable Indicates the first The discrete variable and the first The contribution of the interaction effect of each discrete variable; S2.7, Contribution of the main effects to all discrete variables Sort in descending order and set the main effect screening threshold to [value]. The higher the ranking of the discrete variable, the greater its impact on the target. Variables that meet the criteria are selected. Candidate set of main effect discrete variables with threshold requirements Subsequently, the contribution of the interaction effect to all discrete variables. Sort in descending order and set the interactive effect screening threshold to [value]. Filter out those that meet the requirements For high-contribution interaction parameter pairs that meet the threshold requirements, extract all parameters from the high-contribution interaction parameter pairs to form a candidate set of discrete variables for interaction effects. ,Pick and The union of these sets yields the set of high-impact discrete variables. If the candidate set of discrete variables for interaction effects The parameters in were not entered. However, if it exists in multiple high-contribution interaction parameter pairs, then it will be added to the list. This ensures that both the core parameters dominated by the main effect and the key correlation parameters dominated by the interaction effect are taken into account.

[0026] S3, based on a set of high-impact continuous variables and a set of high-impact discrete variables, generates candidate sets of continuous and discrete variables through a diversity potential-driven evolutionary mechanism and a statistical probability-driven mutation strategy, respectively, and obtains a candidate guide set through individual pairing.

[0027] The specific steps of step S3 are as follows: S3.1, for populations containing only high-influence continuous variables, using the static stiffness objective function of the linear guide rail as the core, sorts the current generation of continuous variable populations in descending order, and uses the Epsilon constraint method to sort the current generation of populations... Extract three individual sets , , The specific formula for the Epsilon constraint method is as follows: , In the above formula, Indicates the current generation population The extraction level is A collection of individuals Indicates the contemporary population individuals, Indicates the contemporary population The total number of individuals, Indicates the level as The constraint threshold of the individual set, Represented as an individual The serial numbers are sorted in descending order of static stiffness. Indicates the level as The constraint threshold of the individual set, where The value is 0.1. The value is 0.2. The value is 0.3; S3.2, from each individual set In sequence, an individual is randomly selected as the reference individual vector for the optimal, second-optimal, and third-optimal static stiffness values. Then, a diversity potential-driven evolutionary mechanism is designed, which includes three evolutionary operations, namely the vectors of each of the remaining ordinary individuals. Based on the reference individual vector Evolutionary operations are performed in each direction to generate three candidate guideway positions. The evolutionary operation formula for each reference individual vector is as follows: , , , , In the above formula, Indicates to The first level of learning Candidate guide rail position, Indicates to The first level of learning Candidate guide rail position, Indicates to The first level of learning Candidate guide rail position, This indicates that the location needs to be updated. Substitute ordinary individual vectors, Indicates from A collection of individuals of a certain level The optimal linear guide individual randomly selected from the pool, i.e. , Indicates from A collection of individuals of a certain level The suboptimal linear guide individual randomly selected from the pool, i.e. , Indicates from A collection of individuals of a certain level The third best linear guide individual randomly selected from the pool, i.e. , and They represent the corresponding The first and second random coefficients are hierarchical and independent of each other. Indicates the first The convergence factor of the generation, Indicates the current iteration number. Indicates the maximum number of iterations; S3.3, based on the three candidate guide rail positions, the potential of each candidate guide rail is determined according to fitness calculation. Based on the objective function of maximizing static stiffness, the objective function of static stiffness is integrated with the constraint conditions composed of maximum contact stress constraint and weight constraint. A comprehensive fitness function is constructed based on the penalty coefficient, which serves as the evaluation benchmark for the potential of the candidate guide rail. The specific formula is as follows: , In the above formula, Indicates by The fitness function guides the evolutionary direction; the smaller the fitness value, the better the potential of the guided individual. Indicates from The static stiffness value of a guide rail individual randomly selected from the set of individuals of the grade. Indicates from The guide rail individuals are randomly selected again from the set of individuals of the grade, among which , This indicates finding the maximum value. Indicates the maximum contact stress threshold. express The corresponding maximum contact stress, Indicates the weight threshold. express The corresponding weight, This represents the penalty coefficient used to quantify the effect of maximum contact stress on individual fitness. This represents the penalty coefficient used to quantify the effect of weight on an individual's fitness. S3.4, based on the fitness function value for each evolutionary direction, calculate the weight coefficients of the candidate orbital positions obtained through the three evolutionary operations, where... The formula for calculating the weighting coefficients is as follows: In the above formula, Indicates the use of quantization The weighting coefficients, Indicates by Fitness values ​​that guide evolutionary direction based on level. Indicates by Fitness values ​​that guide evolutionary direction based on level. Indicates by Fitness values ​​guide the evolutionary direction based on rank; weight coefficients are obtained for other candidate orbital positions, and the final evolutionary formula is derived based on these weight coefficients, as follows: , In the above formula, This represents the generation of the first generation guided by each evolutionary direction. The effective child trajectories are obtained, that is, the candidate set of continuous variables. Indicates the first The weighting coefficients of each candidate guide rail position. Indicates the first The generation One candidate guide rail position; S3.5 For a population containing only a set of high-impact discrete variables, sort them in descending order according to the static stiffness target value to form an ordered set of guide rail candidates. Select the top a% of guide rails from the candidate set as the high-quality sample set. S3.6 Based on the obtained high-quality sample set, design a statistical probability-driven mutation strategy. Obtain the probability of each discrete variable in the high-quality sample set by statistically analyzing the frequency of occurrence of each discrete value. Divide the corresponding evolutionary intervals for each discrete value. The probability calculation formula is as follows: , , In the above formula, Indicates the first The i-th discrete variable takes the i-th... The probability of taking a discrete value. Indicates the first The discrete variables are listed first. Choose the first of the high-quality guide rails Frequency of discrete values Indicates the first Before the discrete variables All possible values ​​for a high-quality guide rail This represents the total number of high-quality guide rails selected from the current generation of guide rail library, sorted by static stiffness from largest to smallest. Indicates the first The i-th discrete variable takes the i-th... The cumulative probability for each discrete value. Indicates the first The i-th discrete variable takes the i-th... The cumulative probability of taking a discrete value; S3.7, according to the index of the discrete variable's value, define the evolution interval based on the probability of each discrete variable taking each discrete value. By generating uniformly distributed random numbers The values ​​of the discrete child guide rails on the corresponding discrete variables are determined by interval matching, as expressed by the formula: , In the above formula, Represented as the first Uniformly random numbers within the interval (0,1) generated independently by each discrete variable. Indicates the first The index of the final value selected by a discrete variable in the discrete child guide, i.e., the random number. The first matching when falling into the corresponding evolutionary range Each discrete value index is used to generate a random number from each discrete variable. The set of discrete values ​​that match the generated value index is the candidate set of the discrete variable; S3.8, through individual pairing, matches and integrates the structural features corresponding to discrete variables with the size parameters corresponding to continuous variables to form the first... A complete set of candidate guide rails with unified parameters This ensures that discrete and continuous variables are physically compatible and mechanically matched in terms of the design parameter values.

[0028] S4. Establish a random forest prediction model with objectives and constraints. Select an excellent subset from the candidate guide set through fast non-dominated sorting, and then select the best offspring guide by combining statistical ranking.

[0029] The specific steps of step S4 are as follows: S4.1 Select the guide rail sample dataset that has passed finite element simulation verification as historical samples. Each sample group contains input features and output labels, where the input features are the high-influence mixed variable set of the guide rail. The high-impact continuous variable set and the high-impact discrete variable set are integrated into a high-impact mixed variable set, and the output labels are... ,in This indicates the design parameters of the linear guide. The corresponding static stiffness value at that time This indicates the design parameters of the linear guide. The maximum contact stress corresponding to this time, This indicates the design parameters of the linear guide. The corresponding weight at that time was then used to divide the training set into several parts according to a certain ratio. and test set ; S4.2, construct three independent random forest prediction models RF0, RF1, and RF2 for the target value and constraint index respectively, and train the models. RF0 represents the random forest prediction model for predicting static stiffness value, RF1 represents the random forest prediction model for predicting maximum contact stress, and RF2 represents the random forest prediction model for predicting weight. S4.3 Calculate the coefficients of determination using the test set for the three trained random forest prediction models. Root mean square With mean absolute percentage error If the model's accuracy is not up to standard, supplement with high-discrepancy samples and perform hyperparameter tuning until the model's accuracy meets the standard. S4.4, for the newly generated first... Candidate guide rail set The static stiffness, maximum contact stress, and weight are predicted using a random forest prediction model to obtain the target values ​​and constraint indices for the candidate guide rail set. The predicted target values ​​and constraint indices are then unified into a minimization objective, transforming the problem into a three-objective problem. The predicted values ​​for the three objectives are: ,in This represents the predicted values ​​for the three objectives. Indicates the first in the candidate guide rail set One effective child guide rail, Indicates the first Predicted static stiffness values ​​of an effective descendant guide rail. Indicates the first Predicted maximum contact stress value for each effective descendant guide rail Indicates the first The predicted weight values ​​of each effective child guide rail are used as a benchmark for fast non-dominated sorting, resulting in a sample size of [number missing]. The Excellent sub-generation guide rail set ; S4.5, extract the target prediction values ​​of the excellent subset and perform linear normalization to map each target value to the [0,1] interval, eliminating the differences in dimensionality and order of magnitude between different targets, and ensuring the fairness of the weights of each indicator when selecting the best among multiple targets in the future. The normalization formula is as follows: , In the above formula, Indicates the first The generation The first excellent offspring guide rail in Normalized target value on each objective, Indicates the first The generation The first excellent offspring guide rail in Predicted values ​​for each target express Within the excellent subset The minimum predicted value of each target. express Within the excellent subset The maximum predicted value of each target; S4.6, normalization objective value The set of excellent descendant guide rails is comprehensively evaluated based on statistical ranking. The comprehensive score of each excellent descendant guide rail is calculated according to the scoring formula and sorted in ascending order. The lower the score, the better the comprehensive performance. The scoring formula is as follows: , In the above formula, Indicates the first The generation The overall score of each excellent descendant guide rail ranges from [0,1]. The smaller the value, the better the overall performance of the descendant guide rail. Indicates the first The weighting coefficients of each objective; S4.7 Select the best offspring guide rail with the lowest comprehensive score as the optimal offspring guide rail. If multiple excellent offspring guide rails have the same lowest comprehensive score, store them in a set of equally excellent offspring guide rails. Further filter the optimal offspring guide rail for the current generation using the target value difference formula, where the target value difference formula is as follows: , In the above formula, Indicates iteration to the th The best offspring guide for the generation, This represents the set of outstanding offspring guide rails that have the same minimum overall score. , Indicates the first generation to the first The mean of the three-objective normalized objective values ​​of the three parallel excellent offspring guides is calculated. This indicates the selection of the best child guide set. The minimum mean of the three objective values ​​after normalization.

[0030] S5. Use the simulation model to evaluate the best offspring guide rail, update the database and random forest prediction model, return to step S3, until the index is met, and output the optimal parameter values.

[0031] The specific steps of step S5 are as follows: S5.1, The optimal offspring guide rail is evaluated using the aforementioned simulation model to obtain the optimal offspring guide rail. The corresponding target values ​​and constraint indicators are the static stiffness, maximum contact stress, and weight of the linear guide rail. S5.2, select the best offspring guide rail The corresponding target values ​​and constraint indicators are stored in the database, and the three random forest prediction models are updated based on all individual vectors in the database. S5.3, Determine the optimal offspring guide rail Do the corresponding static stiffness, maximum contact stress, and weight satisfy the optimization requirement of maximizing the static stiffness value under the constraints of minimizing weight and minimizing maximum contact stress? If they do, output the optimal parameter values; otherwise, return to step S3 to continue iterative optimization until the optimization requirements are met and the optimal parameter values ​​are output.

[0032] Example 1 illustrates the optimization performance of the proposed SOMC linear guide design method using a MINLP (Mixed Integer Nonlinear Programming) benchmark example. The expression for the benchmark example, containing one optimization objective and two optimization constraints, is as follows: , , , , In the above formula, This represents finding the minimum value of the objective function over the benchmark example. It is the objective value function of the benchmark example. Represents a hybrid design parameter vector. Indicates the total number of design parameters. Indicates the number of discrete switch variables. Indicates the first A discrete switch variable, with binary values. , Indicates the first A continuous design variable, with a value range , Indicates the first Linear weighting coefficients for continuous design variables, Indicates the first The coefficients of the nonlinear terms when a discrete switch variable is activated. Indicates the first The baseline coefficients of the nonlinear terms corresponding to each discrete switching variable. Indicates the first The exponential decay coefficient corresponding to each discrete switching variable. Indicates the relationship with the first Discrete switching variables Associated continuous design variables, where Indicates indexing of discrete switch variables Mapping to continuous design variable index The mapping function, i.e. , Indicates the first The fixed cost coefficient when a discrete switch variable is activated. Indicates the first The upper bound of a continuous design variable. , Let represent the first type of constraint set and the second type of constraint set, respectively.

[0033] The above benchmark test examples were processed through steps S1 to S5 of the SOMC linear guide design method provided by this invention to obtain experimental results.

[0034] To further illustrate this embodiment, a linear guide SOMC design method from this embodiment is compared with another classic MI-EDDE algorithm. The maximum number of simulation evaluations in this embodiment is set to 1000, and the experimental results are shown in Table 1. Under the same number of simulation samples, the method of this embodiment obtains the result with the minimum objective function value and is significantly better than MI-EDDE. It can be considered that the method of this embodiment has good performance in the single-objective multi-constraint (SOMC) design problem of maximizing static stiffness, weight, and stress constraints of linear guides.

[0035] Table 1. Comparison of optimization results of different methods

[0036] This invention provides a linear guide SOMC design method, which designs a co-evolutionary strategy based on diversified potential-driven and probability-driven approaches. It can optimize single-objective multi-constraint problems with mixed variables and complex simulations, achieving higher accuracy and better overall performance. It provides a systematic solution for SOMC design of linear guide structures with stiffness as the objective and maximum contact stress and weight as constraints.

[0037] In a second aspect, the present invention provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of a linear guide SOMC design method of the foregoing embodiments.

[0038] The memory can be volatile or non-volatile, or a combination of both. Non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. Volatile memory can be random access memory (RAM), used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), Synchronous DRAM (SDRAM), Double Data Rate SDRAM (DDRSDRAM), Enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM), and Direct Rambus RAM (DRRAM). The memory of this invention is intended to include, but is not limited to, these and any other suitable types of memory.

[0039] The processor can be an integrated circuit chip with signal processing capabilities. In implementation, each step of the above method can be completed by integrated logic circuits in the processor's hardware or by instructions in software form. The processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in this invention. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in this invention can be directly embodied in the execution of a hardware decoding processor, or executed by a combination of hardware and software modules in the decoding processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory; the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method.

[0040] The method steps of this invention can be implemented in hardware, software, firmware, middleware, microcode, or a combination thereof. For hardware implementation, the processing unit can be implemented in one or more application-specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field-programmable gate arrays (FPGAs), general-purpose processors, controllers, microcontrollers, microprocessors, other electronic units for performing the functions described in this application, or combinations thereof.

[0041] Software implementation can be achieved by executing functional modules (such as procedures, functions, etc.). Software code can be stored in memory and executed by the processor. Memory can be implemented in the processor or outside the processor.

[0042] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of a linear guide SOMC design method of the foregoing embodiments.

[0043] Computer storage media can include various media that can store program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0044] Fourthly, the present invention provides a computer program product, including a computer program that, when executed by a processor, implements the steps of a linear guide SOMC design method according to the foregoing embodiments.

[0045] Specifically, computer program products include: data signals and data signals embodied in a carrier wave.

[0046] It should be noted that the technical solutions described in this invention can be combined arbitrarily without conflict.

[0047] Those skilled in the art will readily understand that the above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A design method for a linear guide SOMC, characterized in that, include: S1 uses the linear guide rail dimensions (continuous variables) and material type, preload level, and number of sliders and balls (discrete variables) as design parameters. Based on structural characteristics and static load analysis, a simulation model and SOMC design model are constructed with static stiffness as the objective and weight and maximum contact stress as constraints. S2. Construct a design space based on the range of design parameters, generate an initial population and establish a database using chaotic strategy and full factorial design, and obtain the set of high-impact continuous variables and the set of high-impact discrete variables respectively through SRC and CEA sensitivity analysis methods. S3, based on a set of high-impact continuous variables and a set of high-impact discrete variables, generates candidate sets of continuous and discrete variables through a diversity potential-driven evolutionary mechanism and a statistical probability-driven mutation strategy, respectively, and obtains a candidate guide set through individual pairing; S4. Establish a random forest prediction model with objectives and constraints. Select an excellent subset from the candidate guide set through fast non-dominated sorting, and then select the best offspring guide by combining statistical ranking method. S5. Use the simulation model to evaluate the best offspring guide rail, update the database and random forest prediction model, return to step S3, until the index is met, and output the optimal parameter values.

2. The method as described in claim 1, characterized in that, Step S1 specifically includes: S1.1, combining the structural characteristics of linear guide rails, the slider length, slider width, slider height, raceway curvature radius, raceway center distance, initial contact angle, raceway groove depth, ball diameter, guide rail length, guide rail width, and guide rail height are taken as continuous variables, while the number of balls, number of sliders, material type, and preload level are taken as discrete variables. The continuous and discrete variables are used as design parameters. S1.2, Based on the load conditions of the linear guide structure, a three-dimensional model is constructed using the three-dimensional modeling software Catia and parameterized to obtain a parameterized model; S1.3, import the parametric model, the load conditions of the linear guide structure and the key boundary conditions into the finite element analysis pre- and post-processing software Ansys Workbench for finite element analysis to obtain the finite element analysis model; S1.

4. Using the solver of the structural optimization and multiphysics simulation software, static load analysis is performed on the finite element analysis model to obtain the static stiffness, maximum contact stress and weight simulation model of the linear guide rail. S1.5, Based on the simulation model of static stiffness, maximum contact stress, and weight of the linear guide, the SOMC design model of the linear guide is constructed with static stiffness as the objective and maximum contact stress and weight as constraints. The specific expressions are as follows: ， ， ， In the above formula, This indicates the search for the optimal solution to the design parameters. This indicates the design parameters of the linear guide. Indicates the length of the slider. Indicates the height of the slider. Indicates the slider width. Indicates the radius of curvature of the raceway. Indicates the center distance of the raceways. Indicates the initial contact angle. Indicates the depth of the raceway groove. Indicates the length of the guide rail. Indicates the guide rail height. Indicates the width of the guide rail. Indicates the diameter of the ball bearing. Indicates the number of balls. Indicates the number of sliders. Indicates the material type. Indicates the preload level. This indicates finding the maximum value. This indicates the design parameters of the linear guide. The corresponding static stiffness at that time This indicates the design parameters of the linear guide. The corresponding static stiffness function at time, This represents the constraints that the linear guide rail must satisfy regarding its weight and maximum contact stress. This indicates the design parameters of the linear guide. The maximum contact stress corresponding to this time, Indicates the maximum contact stress threshold. This indicates the design parameters of the linear guide. The corresponding weight at that time This indicates the weight threshold.

3. The method as described in claim 1, characterized in that, Step S2 specifically includes: S2.1, Determine the range of values ​​for continuous variables and the set of values ​​for discrete variables according to design requirements, and construct continuous design space and discrete design space respectively; S2.2 An initial population of discrete variables is generated in the discrete design space using full factorial design, and an initial population of continuous variables is generated in the continuous design space using a chaotic strategy. The discrete and continuous variable populations constitute the initial population, where the chaotic sequence is generated by the Tent mapping criterion. Different initial chaotic sequence values ​​are designed for each design parameter of each continuous variable. The initial chaotic sequence value is iteratively updated, and the next chaotic sequence value is obtained through piecewise calculation. The formula for calculating chaotic sequences is as follows: ， ， In the above formula, Indicates the first The nth continuous variable Chaotic sequence values ​​corresponding to each design parameter This represents the Tent mapping criterion function. Indicates the first The nth continuous variable Chaotic sequence values ​​corresponding to each design parameter This represents the chaotic sequence mapped to the initial population. Indicates the initial population size. Indicates the dimension of the initial population; S2.3, with the optimization objective of maximizing static stiffness and the constraints of the maximum contact stress not exceeding the maximum contact stress threshold and the weight not exceeding the weight threshold, the initial population is simulated and evaluated using the static stiffness function, maximum contact stress function, and weight function of the linear guide. The obtained static stiffness, maximum contact stress, and weight data of the linear guide are used as real samples to establish a database. Then, the initial population is divided into a set of preprocessed continuous variables and a set of preprocessed discrete variables. For the two sets of variables, the target values ​​of their corresponding parameters and the output response sets of each constraint index are determined respectively. S2.4, For the preprocessed continuous variable set, based on the SRC sensitivity analysis method, firstly, each continuous variable is standardized. Then, a linear regression model is constructed using the output response set of the preprocessed continuous variables as the dependent variable and the standardized continuous variables as the independent variables. The regression coefficients are obtained by fitting the linear regression model using the least squares method. The formulas for the standardization operation and the linear regression model are as follows: ， ， In the above formula, Indicates the first Standardized values ​​of a continuous variable. No. The original observations of a continuous variable, Indicates the first The mean of a continuous variable, Indicates the first The sample standard deviation of a continuous variable. This represents the set of outputs corresponding to a sample containing all preprocessed continuous variables. This represents a linear regression model that includes all preprocessed continuous variables. This represents the intercept of the linear regression model. Indicates the first Standard regression coefficients of continuous variables Indicates the number of continuous variables. Represents the residuals of a linear regression model; S2.5, the obtained standard regression coefficients Take the absolute value, then sort in descending order. Based on engineering experience, set the threshold for the regression coefficients of continuous variables as follows: A higher ranking indicates a greater impact of the continuous variable on the output; therefore, those that meet the criteria are selected. High-impact continuous variable set with threshold requirements ; S2.6, For the preprocessed set of discrete variables, based on the CEA sensitivity analysis method, the sum of squares of the main effects of each discrete variable is calculated according to the output response set. and the sum of squares of the interaction effects between the two discrete variables. The contribution of each discrete variable is calculated from the sum of squares of the two effects. The CEA sensitivity analysis formula is as follows: ， ， ， In the above formula, Indicates the first Sum of squares of the main effects of discrete variables Indicates the first The i-th discrete variable The static stiffness value of the guide rail at each level. Indicates the first The number of experiments at a certain level for a discrete variable. Indicates the first under all experimental combinations The static stiffness value of the guide rail at each level. Indicates the total number of experiments. Indicates the first The expression for the between-group variance of discrete variables. No. The discrete variable and the first The sum of squares of the interaction effects of discrete variables, Indicates the first The discrete variable and the first The first discrete variable combination The static stiffness value of the guide rail at each level. Indicates the first The discrete variable and the first The number of experiments at a certain level under a combination of discrete variables. Indicates the first The i-th discrete variable The static stiffness value of the guide rail at each level. This represents the total variance including all preprocessed discrete variables. Indicates the first The main effect contribution of each discrete variable Indicates the first The discrete variable and the first The contribution of the interaction effect of each discrete variable; S2.7, Contribution of the main effects to all discrete variables Sort in descending order and set the main effect screening threshold to [value]. The higher the ranking of the discrete variable, the greater its impact on the target. Variables that meet the criteria are selected. Candidate set of main effect discrete variables with threshold requirements Subsequently, the contribution of the interaction effect to all discrete variables. Sort in descending order and set the interactive effect screening threshold to [value]. Filter out those that meet the requirements For high-contribution interaction parameter pairs that meet the threshold requirements, extract all parameters from the high-contribution interaction parameter pairs to form a candidate set of discrete variables for interaction effects. ,Pick and The union of these sets yields the set of high-impact discrete variables. If the candidate set of discrete variables for interaction effects The parameters in were not entered. However, if it exists in multiple high-contribution interaction parameter pairs, then it will be added to the list. This ensures that both the core parameters dominated by the main effect and the key correlation parameters dominated by the interaction effect are taken into account.

4. The method as described in claim 1, characterized in that, Step S3 specifically includes: S3.1, for populations containing only high-influence continuous variables, using the static stiffness objective function of the linear guide rail as the core, sorts the current generation of continuous variable populations in descending order, and uses the Epsilon constraint method to sort the current generation of populations... Extract three individual sets , , The specific formula for the Epsilon constraint method is as follows: ， In the above formula, Indicates the current generation population The extraction level is A collection of individuals Indicates the contemporary population individuals, Indicates the contemporary population The total number of individuals, Indicates the level as The constraint threshold of the individual set, Represented as an individual The serial numbers are sorted in descending order of static stiffness. Indicates the level as The constraint threshold of the individual set, where The value is 0.

1. The value is 0.

2. The value is 0.3; S3.2, from each individual set In sequence, an individual is randomly selected as the reference individual vector for the optimal, second-optimal, and third-optimal static stiffness values. Then, a diversity potential-driven evolutionary mechanism is designed, which includes three evolutionary operations, namely the vectors of each of the remaining ordinary individuals. Based on the reference individual vector Evolutionary operations are performed in each direction to generate three candidate guideway positions. The evolutionary operation formula for each reference individual vector is as follows: ， ， ， ， In the above formula, Indicates to The first level of learning Candidate guide rail position, Indicates to The first level of learning Candidate guide rail position, Indicates to The first level of learning Candidate guide rail position, This indicates that the location needs to be updated. Substitute ordinary individual vectors, Indicates from A collection of individuals of a certain level The optimal linear guide individual randomly selected from the pool, i.e. , Indicates from A collection of individuals of a certain level The suboptimal linear guide individual randomly selected from the pool, i.e. , Indicates from A collection of individuals of a certain level The third best linear guide individual randomly selected from the pool, i.e. , and They represent the corresponding The first and second random coefficients are hierarchical and independent of each other. Indicates the first The convergence factor of the generation, Indicates the current iteration number. Indicates the maximum number of iterations; S3.3, based on the three candidate guide rail positions, the potential of each candidate guide rail is determined according to fitness calculation. Based on the objective function of maximizing static stiffness, the objective function of static stiffness is integrated with the constraint conditions composed of maximum contact stress constraint and weight constraint. A comprehensive fitness function is constructed based on the penalty coefficient, which serves as the evaluation benchmark for the potential of the candidate guide rail. The specific formula is as follows: ， In the above formula, Indicates by The fitness function guides the evolutionary direction; the smaller the fitness value, the better the potential of the guided individual. Indicates from The static stiffness value of a guide rail individual randomly selected from the set of individuals of the grade. Indicates from The guide rail individuals are randomly selected again from the set of individuals of the grade, among which , This indicates finding the maximum value. Indicates the maximum contact stress threshold. express The corresponding maximum contact stress, Indicates the weight threshold. express The corresponding weight, This represents the penalty coefficient used to quantify the effect of maximum contact stress on individual fitness. This represents the penalty coefficient used to quantify the effect of weight on an individual's fitness. S3.4, based on the fitness function value for each evolutionary direction, calculate the weight coefficients of the candidate orbital positions obtained through the three evolutionary operations, where... The formula for calculating the weighting coefficients is as follows: In the above formula, Indicates the use of quantization The weighting coefficients, Indicates by Fitness values ​​that guide evolutionary direction based on level. Indicates by Fitness values ​​that guide evolutionary direction based on level. Indicates by Fitness values ​​guide the evolutionary direction based on rank; weight coefficients are obtained for other candidate orbital positions, and the final evolutionary formula is derived based on these weight coefficients, as follows: ， In the above formula, This represents the generation of the first generation guided by each evolutionary direction. The effective child trajectories are obtained, that is, the candidate set of continuous variables. Indicates the first The weighting coefficients of each candidate guide rail position. Indicates the first The generation One candidate guide rail position; S3.5 For a population containing only a set of high-impact discrete variables, sort them in descending order according to the static stiffness target value to form an ordered set of guide rail candidates. Select the top a% of guide rails from the candidate set as the high-quality sample set. S3.6 Based on the obtained high-quality sample set, design a statistical probability-driven mutation strategy. Obtain the probability of each discrete variable in the high-quality sample set by statistically analyzing the frequency of occurrence of each discrete value. Divide the corresponding evolutionary intervals for each discrete value. The probability calculation formula is as follows: ， ， In the above formula, Indicates the first The i-th discrete variable takes the i-th... The probability of taking a discrete value. Indicates the first The discrete variables are listed first. Choose the first of the high-quality guide rails Frequency of discrete values Indicates the first Before the discrete variables All possible values ​​for a high-quality guide rail This represents the total number of high-quality guide rails selected from the current generation of guide rail library, sorted by static stiffness from largest to smallest. Indicates the first The i-th discrete variable takes the i-th... The cumulative probability for each discrete value. Indicates the first The i-th discrete variable takes the i-th... The cumulative probability of taking a discrete value; S3.7, according to the index of the discrete variable's value, define the evolution interval based on the probability of each discrete variable taking each discrete value. By generating uniformly distributed random numbers The values ​​of the discrete child guide rails on the corresponding discrete variables are determined by interval matching, as expressed by the formula: ， In the above formula, Represented as the first Uniformly random numbers within the interval (0,1) generated independently by each discrete variable. Indicates the first The index of the final value selected by a discrete variable in the discrete child guide, i.e., the random number. The first matching when falling into the corresponding evolutionary range Each discrete value index is used to generate a random number from each discrete variable. The set of discrete values ​​that match the generated value index is the candidate set of the discrete variable; S3.8, through individual pairing, matches and integrates the structural features corresponding to discrete variables with the size parameters corresponding to continuous variables to form the first... A complete set of candidate guide rails with unified parameters This ensures that discrete and continuous variables are physically compatible and mechanically matched in terms of the design parameter values.

5. The method as described in claim 1, characterized in that, Step S4 specifically includes: S4.1 Select the guide rail sample dataset that has passed finite element simulation verification as historical samples. Each sample group contains input features and output labels, where the input features are the high-influence mixed variable set of the guide rail. The high-impact continuous variable set and the high-impact discrete variable set are integrated into a high-impact mixed variable set, and the output labels are... ,in This indicates the design parameters of the linear guide. The corresponding static stiffness value at that time This indicates the design parameters of the linear guide. The maximum contact stress corresponding to this time, This indicates the design parameters of the linear guide. The corresponding weight at that time was then used to divide the training set into several parts according to a certain ratio. and test set ; S4.2, construct three independent random forest prediction models RF0, RF1, and RF2 for the target value and constraint index respectively, and train the models. RF0 represents the random forest prediction model for predicting static stiffness value, RF1 represents the random forest prediction model for predicting maximum contact stress, and RF2 represents the random forest prediction model for predicting weight. S4.3 Calculate the coefficients of determination using the test set for the three trained random forest prediction models. Root mean square With mean absolute percentage error If the model's accuracy is not up to standard, supplement with high-discrepancy samples and perform hyperparameter tuning until the model's accuracy meets the standard. S4.4, for the newly generated first... Candidate guide rail set The static stiffness, maximum contact stress, and weight are predicted using a random forest prediction model to obtain the target values ​​and constraint indices for the candidate guide rail set. The predicted target values ​​and constraint indices are then unified into a minimization objective, transforming the problem into a three-objective problem. The predicted values ​​for the three objectives are: ,in This represents the predicted values ​​for the three objectives. Indicates the first in the candidate guide rail set One effective child guide rail, Indicates the first Predicted static stiffness values ​​of an effective descendant guide rail. Indicates the first Predicted maximum contact stress value for each effective descendant guide rail Indicates the first The predicted weight values ​​of each effective child guide rail are used as a benchmark for fast non-dominated sorting, resulting in a sample size of [number missing]. The Excellent sub-generation guide rail set ; S4.5, extract the target prediction values ​​of the excellent subset and perform linear normalization to map each target value to the [0,1] interval, eliminating the differences in dimensionality and order of magnitude between different targets, and ensuring the fairness of the weights of each indicator when selecting the best among multiple targets in the future. The normalization formula is as follows: ， In the above formula, Indicates the first The generation The first excellent offspring guide rail in Normalized target value on each objective, Indicates the first The generation The first excellent offspring guide rail in Predicted values ​​for each target express Within the excellent subset The minimum predicted value of each target. express Within the excellent subset The maximum predicted value of each target; S4.6, normalization objective value The set of excellent descendant guide rails is comprehensively evaluated based on statistical ranking. The comprehensive score of each excellent descendant guide rail is calculated according to the scoring formula and sorted in ascending order. The lower the score, the better the comprehensive performance. The scoring formula is as follows: ， In the above formula, Indicates the first The generation The overall score of each excellent descendant guide rail ranges from [0,1]. The smaller the value, the better the overall performance of the descendant guide rail. Indicates the first The weighting coefficients of each objective; S4.7 Select the best offspring guide rail with the lowest comprehensive score as the optimal offspring guide rail. If multiple excellent offspring guide rails have the same lowest comprehensive score, store them in a set of equally excellent offspring guide rails. Further filter the optimal offspring guide rail for the current generation using the target value difference formula, where the target value difference formula is as follows: ， In the above formula, Indicates iteration to the th The best offspring guide for the generation, This represents the set of outstanding offspring guide rails that have the same lowest overall score. , Indicates the first generation to the first The mean of the three-objective normalized objective values ​​of the three parallel excellent offspring guides is calculated. This indicates the selection of the best child guide set. The minimum mean of the three objective values ​​after normalization.

6. The method as described in claim 1, characterized in that, Step S5 specifically includes: S5.1, The optimal offspring guide rail is evaluated using the aforementioned simulation model to obtain the optimal offspring guide rail. The corresponding target values ​​and constraint indicators are the static stiffness, maximum contact stress, and weight of the linear guide rail. S5.2, select the best offspring guide rail The corresponding target values ​​and constraint indicators are stored in the database, and the three random forest prediction models are updated based on all individual vectors in the database. S5.3, Determine the optimal offspring guide rail Do the corresponding static stiffness, maximum contact stress, and weight satisfy the optimization requirement of maximizing the static stiffness value under the constraints of minimizing weight and minimizing maximum contact stress? If they do, output the optimal parameter values; otherwise, return to step S3 to continue iterative optimization until the optimization requirements are met and the optimal parameter values ​​are output.

7. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1-6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1-6.

9. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1-6.

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